Adding Transitivity and Counting to the Fluted Fragment

We study the impact of adding both counting quantifiers and a single transitive relation to the fluted fragment - a fragment of first-order logic originating in the work of W.V.O. Quine. The resulting formalism can be viewed as a multi-variable, non-guarded extension of certain systems of description logic featuring number restrictions and transitive roles, but lacking role-inverses. We establish the finite model property for our logic, and show that the satisfiability problem for its k-variable sub-fragment is in (k+1)-NExpTime. We also derive ExpSpace-hardness of the satisfiability problem for the two-variable, fluted fragment with one transitive relation (but without counting quantifiers), and prove that, when a second transitive relation is allowed, both the satisfiability and the finite satisfiability problems for the two-variable fluted fragment with counting quantifiers become undecidable

Answering regular path queries mediated by unrestricted SQ ontologies

A prime application of description logics is ontology-mediated query answering, with the query language often reaching far beyond instance queries. Here, we investigate this task for positive existential two-way regular path queries and ontologies formulated in the expressive description logic , where denotes the extension of the basic description logic with transitive roles () and qualified number restrictions () which can be unrestrictedly applied to both non-transitive and transitive roles (). Notably, the latter is usually forbidden in expressive description logics. As the main contribution, we show decidability of ontology-mediated query answering in that setting and establish tight complexity bounds, namely 2ExpTime-completeness in combined complexity and coNP-completeness in data complexity. Since the lower bounds are inherited from the fragment , we concentrate on providing upper bounds. As main technical tools we establish a tree-like countermodel property and a characterization of when a query is not satisfied in a tree-like interpretation. Together, these results allow us to use an automata-based approach to query answering

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas